I grow it in pots and it seems to do alright.. no critters attack it that way. But if it is growing in ground now, how about trying one of the tomato cages ( you know those metal thingies you let tomato plants grow up on)? perhaps by putting that around it , it will be protected.
Maybe there is a bunny around ( or squirrel) who has a pesto diet.

Now what I need is a new lawn.. any landscaper recommendations? :p